Not sure if it's called "curves" in English, but what I am refering to is graphs that repeat over a given time.(adsbygoogle = window.adsbygoogle || []).push({});

ie

f(x) = sin(x)

The problem I am having is understanding the following:

Given:

f(x) = sin(x)

g(x) = cos(x)

Find f(x) - g(x) by A(cos(x - x0)).

Which gives:

A(cos(x - x0)) = A(cos(x0))cos(x) + A(sin(x0))sin(x)

A(cos(x0)) = 1

A(sin(x0)) = -1

thus:

A = sqrt(1^2 + (-1)^2) = 1

Finding x0:

tan wx0 = 1/(-1)

1*x0 = arctan(-1)

x0 = -0.79

Here I'm pretty much lost. I've probably done some mistakes along the way as well :(

What is -0.79? x0 is supposed to be the 'top' of the curve right?

ie to find every top, you would have something like:

x0 +/- |n|*2PI

Where n is a whole number(1..inf) and 2PI would be the period of each "curve".

Could someone explain this to me, I'm trying to learn this by just reading a book and I'm having a hard time.

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# Harmonic curves

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